Area of a circular segment is $77$ sq m and radius is $21$ m. The central angle is —

From area $=\frac{\theta}{360°}\pi r^{2}$, solve $\theta=\frac{360°\times A}{\pi r^{2}}=\frac{360\times 77}{\pi\times 21^{2}}\approx 20°$. The given area and radius fix the central angle.